Abstract
A reliable Jacobi-like method for the problem Sx = λTx has been presented where S and T are real, symmetric but indefinite, and T has the same number of positive and negative eigenvalues as it occurs in standard problems of damped oscillations of structures. The method is quadratically convergent in all non-defective cases including also the cases of double defective real eigenvalues which correspond to the physically important phenomenon of critical damping. The symmetry is preserved in all stages which carries a 50% saving of both computing time and space. The experimental comparison with the QR method and the standard complex method of Eberlein has been made. The present method has shown to be particularly suitable for diagonally dominant matrices as they appear e.g. in subspace iterations.
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